A Comparison of p-adic Motivic Cohomology and Rigid Cohomology

Author: Lawless Hughes, Nathaniel

Year: 2019

Degree: Dissertation (Ph.D.)

Advisor: Flach, Matthias

Committee Members: Mantovan, Elena; Flach, Matthias; Ramakrishnan, Dinakar; Zhu, Xinwen

Option: Mathematics

DOI: 10.7907/DCJJ-E164

Abstract

We study two conjectures introduced by Flach and Morin in [FM18] for schemes over a perfect field of characteristic p > 0. The first conjecture relates a p-adic extension of the étale motivic cohomology with compact support on general schemes introduced by Geisser in [Gei06] to rigid cohomology with compact support, and is proved here. The second, relates a p-adic Borel-Moore motivic homology with the dual of rigid cohomology with compact support, and is proved in the smooth case. For this, we also prove a generalization of the comparison theorem from rigid cohomology to overconvergent de Rham-Witt cohomology in [DLZ11].

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